Can you make a case for why a supernatural origin for the image on the cloth is more believable than forgery?
Your implausible idea is based on a lot of assumptions. That would be the first hurdle. For example, why wouldn’t a forger know about the actual process of crucifixion? Why wouldn’t the forger know about serum rings, or use real blood? You also assume that the limestone is from Jerusalem, that it is rare, or that the forger wouldn’t have access to it. For all we know, the forger created it in Jerusalem. It is assumed that the sewing technique was only used in the 1st century, or that the forger wouldn’t know about it. Adding discoloration to fake an age is one of the oldest tricks in the book for a forger.
Also, there were tons of forgeries of different relics circulating at the time. Even if there was a real relic out there, the chances of having the real one is much lower than having a fake one.